Hey Economyst can you please help with the following microeconomics question, have tried but getting no where.

Question

Q: a demand function for a economics book is P = 100 - 0.005Q

the publisher must pay $20 per book in prinitng and distribution costs and in addition it must pay the author $20 royalty for each book sold

a) your job is to provide advice to the publisher. what price will maximise the publishers profit ? how mush profit will the publisher earn ? what will be the total royalty payment earned by the author ?

b) a consultant says that the publisher and the author have the wrong type of agreement. he says the author and the publisher should tear up hteir original agreement, in which the author gets $20 per book sold, and enter into profit-sharing agreement. he recommends that the author gets 40% of the profit and the publisher gets 60%. what price should the publisher set with this profit-sharing agreement ?

c) will both the author and the publisher prefer the profit-sharing agreement to their original agreement ? which agreement will the students who buy the textbook prefer ?

d) given the demand and cost conditions indicated above suppose thath the royalty payment was such that the author received a payment which was 15% of sales revenue. prpve that there is an inherent conflict between the author and publisher in that the auhtor has an interest in the book's price being lower than the price which maximises the publisher's profit.

A "Danial B" and a "Tinky" asked this same question last friday. Below is my post to Tinky. The basic solution to all sub-problems is to find the quantity Q where Marginal Cost=Marginal Revenue.
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Friday the 13th post:

Total revenue is P*Q. = 100Q-.005Q² . Marginal revenue is the first derivitive of total revenue, so MR=100-.01Q

Marginal cost is the cost, to the publisher, of producing 1 additional book. He pays $20 printing costs plus $20 royalities for each book, regardless of the number printed. Ergo, Marginal Cost = Average cost = $40.

Solve MR=MC = 100-.01Q=40 Q=6000.
For you, calculate optimal price, the net profit going to the publisher and the royalities going to the author.

b) Now things get a bit tricky. The publisher must still pay $20 for printing. However, under the new contract, he pays 40% of the net profit. So, Marginal cost becomes 20 + .4*(P-20) = 12+.4*P. Substitute the original demand equation for P. Thus MC=12+.4*(100-.001Q) = 52-.002Q.
Again, set MC=MR and solve for Q.

c) Again calculate the amounts going to the publisher and author. Compare these to the amounts you calculated for part a). Compare the prices, as well, to see which plan the students will prefer.

d) With a flat 15% of sales, the marginal cost for the publisher becomes 20+.15P Repeat the steps you did in b). The inherent conflict arises because the publisher must pay the printing costs, while the marginal cost for the author is zero.

It appears I have a typo in b) MC should be 52 - .004Q. Sorry for the inconvenience.

Check that again. I had the MC in b) right the first time, but I mistyped the part where I substituted the demand curve for P. MC=12+.4*(100-.005Q) = 52-.002Q.

Hopefully no more mistypes on my part.